It could be that the theme where errors are occurring is trying to reference an Author's Profile, but a profile doesn't exist, and the code in that theme isn't checking to see if the author's profile is null.
For example, in the Standard theme that ships with BE 1.6, there's this code in PostView.ascx.
Post.AuthorProfile != null ? Post.AuthorProfile.DisplayName : Post.Author
It uses the profile DisplayName if the profile exists, otherwise, it displays the plain old author name.
The theme that is having problems, might just be doing something like:
without checking to see if Post.AuthorProfile is null.
I would search the theme's files for "AuthorProfile".